Finite Group Databasebeta

← D11×#1355 #14664942

Subgroups — D11×#1355 #14664942

Order 2816.

366 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#490C211yesmaximal, characteristic
2D11×#347C212yesmaximal, complemented
3#13066649C211yesmaximal, characteristic, complemented
4#13066648C212yesmaximal, complemented
5C11×#1355C211yesmaximal, characteristic, complemented
6D11×#127C411yescharacteristic
7D11×#125C411yescharacteristic
8C11×#490C2211yescharacteristic
9#10622684C411yescharacteristic
10#10622680C411yescharacteristic
11D11×M32—22no—
12D11×#102—22no—
13#10622377—22no—
14#10622326C2211yescharacteristic
15D11×#97C2211yescharacteristic
16C11×#347C2212yescomplemented
17#10622150—22no—
18#10622104C2212yescomplemented
19C2×D4×D11—21no—
20C2×D4×D11—41no—
21C11×#127C2×C411yescharacteristic
22C11×#125C2×C411yescharacteristic
23#66993—21no—
24#66993—41no—
25C2×C8×D11D412yes—
26C4⋊C4×D11—21no—
27C4⋊C4×D11—41no—
28#66943—21no—
29#66942—41no—
30#66927C2×C411yescharacteristic
31C42×D11C2×C411yescharacteristic
32#66923C2×C411yescharacteristic
33C11×M32—22no—
34C11×#102—22no—
35C11×#97C2311yescharacteristic
36#66896—22no—
37#66885—22no—
38#66879D412yes—
39#66876—22no—
40#66873—22no—
41#66867C2×C411yescharacteristic
42#66862—24no—
43C16×D11—24no—
44C2×#1355—111nomaximal, Sylow
45C23×D11—41no—
46C2×D4×C11—21no—
47C2×D4×C11—41no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—41no—
50D4×D11—42no—
51D4×D11—42no—
52D4×D11—84no—
53C2×D44—21no—
54C2×D44—41no—
55C2×C4×D11—21no—
56C2×C4×D11—41no—
57C2×C4×D11C22⋊C411yescharacteristic
58C2×C8×C11C2×D412yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—41no—
61C42×C11C22×C411yescharacteristic
62C4⋊Dic11—21no—
63C4⋊Dic11—41no—
64Dic11⋊C4—41no—
65Dic11⋊C4—41no—
66Dic11⋊C4—41no—
67C4×Dic11—21no—
68C4×Dic11C22⋊C411yescharacteristic
69C2×C11⋊C8C22⋊C412yes—
70C8×D11—22no—
71C8×D11—22no—
72C11×C16—24no—
73C11⋊C16—24no—
74C2×#490—111no—
75C2×#347—112no—
76#1355—111no—
77#1355—112no—
78#1355D1111yescharacteristic, direct product factor
79C23×C11—41no—
80C22×D11—41no—
81C22×D11—84no—
82C22×D11—81no—
83C22×D11—81no—
84C22×D11#10011yescharacteristic
85D4×C11—42no—
86D4×C11—82no—
87C2×C4×C11—21no—
88C2×C4×C11—41no—
89C2×C4×C11C2×C22⋊C411yescharacteristic
90C22⋊D11—84no—
91C22⋊D11—82no—
92C2×Dic11—21no—
93C2×Dic11—41no—
94C2×Dic11#10011yescharacteristic
95D44—42no—
96D44—82no—
97C4×D11—42no—
98C4×D11—82no—
99C4×D11#10412yes—
100C4×D11#10412yes—
101C8×C11—22no—
102C11⋊C8—22no—
103C2×#127—111no—
104C2×#125—111no—
105C2×M32—222no—
106#490—111no—
107#490—111no—
108#490—111no—
109#490—222no—
110#490C2×D1111yescharacteristic
111C2×#102—222no—
112C2×#97—111no—
113#347—112no—
114#347—222no—
115#347C2×D1112yescomplemented
116C22×C11—82no—
117C22×C11—81no—
118C22×C11C2×#10011yescharacteristic
119C2×D11—22no—
120C2×D11—82no—
121C2×D11—81no—
122C2×D11—162no—
123C2×D11—162no—
124C2×D11#32911yescharacteristic
125C2×D11#32911yescharacteristic
126C4×C11—41no—
127C4×C11—81no—
128C4×C11C2×#10412yes—
129Dic11—41no—
130Dic11—81no—
131Dic11#32912yes—
132C22×D4—221no—
133C22×D4—441no—
134C22×C8—112no—
135#127—111no—
136#127—221no—
137#127—441no—
138#127C4×D1111yescharacteristic
139#125—111no—
140#125—221no—
141#125—441no—
142#125C4×D1111yescharacteristic
143C2×C4⋊C4—221no—
144C2×C4⋊C4—441no—
145C2×C42—111no—
146M32—22no—
147M32—224no—
148M32—222no—
149C2×C16—224no—
150#102—22no—
151#102—222no—
152#102—222no—
153#102—222no—
154#97—112no—
155#97—111no—
156#97C22×D1111yescharacteristic
157C2×C11—21no—
158C2×C11—161no—
159C2×C11C2×#32911yescharacteristic
160D11—21no—
161D11—161no—
162D11#135512yesdirect product factor
163C24—441no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—221no—
167C2×D4—441no—
168C2×D4—442no—
169C2×D4—442no—
170C2×D4—441no—
171C2×D4—442no—
172C2×D4—884no—
173C22×C4—111no—
174C22×C4—221no—
175C22×C4—441no—
176C2×C8—112no—
177C2×C8—222no—
178C2×C8—222no—
179C2×C8D4×D1112yes—
180C4⋊C4—21no—
181C4⋊C4—41no—
182C4⋊C4—221no—
183C4⋊C4—441no—
184C4⋊C4—441no—
185C4⋊C4—441no—
186C4⋊C4—441no—
187C42—111no—
188C42—221no—
189C42C2×C4×D1111yescharacteristic
190C16—24no—
191C16—224no—
192C11C2×#135511yescharacteristic, complemented, Sylow
193C23—41no—
194C23—111no—
195C23—441no—
196C23—881no—
197C23—881no—
198C23—884no—
199D4—42no—
200D4—82no—
201D4—442no—
202D4—882no—
203D4—882no—
204D4—884no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—111no—
208C2×C4—112no—
209C2×C4—112no—
210C2×C4—221no—
211C2×C4—442no—
212C2×C4—441no—
213C2×C4—882no—
214C2×C4C22⋊C4×D1111yescharacteristic
215C8—22no—
216C8—222no—
217C22—82no—
218C22—81no—
219C22—111no—
220C22—111no—
221C22—222no—
222C22—882no—
223C22—881no—
224C22—1762no—
225C22—1762no—
226C22D11×#10011yescharacteristic
227C4—41no—
228C4—81no—
229C4—112no—
230C4—441no—
231C4—881no—
232C4D11×#10412yes—
233C2—21no—
234C2—112no—
235C2—161no—
236C2—221no—
237C2—1761no—
238C2D11×#32911yescharacteristic
subgroupG/H
centerC2D11×#329
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#1355C2
socleC2×C11C2×#329
prime radicalD11×#127C4
cosocleC11×#97C23
hypercenter#1355D11
hypocenterC11C2×#1355
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D11×#347C2semidirect
3. #13066649C2semidirect
4. #13066648C2semidirect
5. C11×#1355C2semidirect
16. C11×#347C22semidirect
18. #10622104C22semidirect
78. #1355D11direct (N × H)
115. #347C2×D11semidirect
162. D11#1355direct (N × H)
192. C11C2×#1355semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D11×#4902
D11×#3472
#130666492
#130666482
C11×#13552
C2×#135511